Sociology

LAURA BOCCI

The educational target of this course is the provision of core competencies geared to the statistical analysis, both descriptive and inferential. Notably, the course will put forward the following subjects: preliminary analysis of data and their graphical representations, descriptive statistics, main techniques of analysis on two variables, regression, correlation, elements of probability and statistical inference.

At the end of the course, students will have an appropriate level of competence in theoretical knowledge of statistical methods, as well as in their practical application. Furthermore, they will be able to apply on their own basic statistical techniques in operating environments, having developed the necessary analytical skills.

Notably, the student will gain a good command of the research method and the techniques currently used, as well as the related practical and operational skills on data measurement, detection and processing, improving its capacity for operational analysis of social and economic variables.

Finally, the student is supposed to be able in applying his knowledge into a real-life work environment, to fulfil tasks in many application areas.

The main aim is to endow students with basic statistical tools for collecting and analysing univariate and bivariate data for political, economic and social sciences applications. Descriptive statistics provide methods for data explorative analysis. Probability theory provides models for phenomena which are subject to uncertainty. Statistical inference provides methods for analysing data obtained from random experiments. Practical lessons dealing with real-world examples are designed to allow students to improve abilities in collecting, analysing, interpreting and presenting findings and data.
Specifically, upon completion of the course the students will have acquired the following skills:
1) Knowledge and understanding: the knowledge of the key tools of Statistics, from the descriptive methodologies to the basic inferential techniques. The knowledge of data types and related univariate analysis techniques (frequency distributions, graphical representations, central tendency and dispersion measures), Probability theory, Statistical inference, association in two-way tables, linear regression.
2) Ability to apply knowledge and understanding: the ability to perform a statistical analysis in the field of social sciences, choosing the most appropriate tools such as tabular and graphical summaries, statistical indexes, inferential procedures.
3) Making judgements: the ability to collect and use quantitative and qualitative data relating to social and economic sciences, and to critically interpret the results obtained using statistical evidence and sound reasoning. This particular competence develops through the presentation of applications and classroom discussions stimulated by the teacher based on analysed examples.
4) Communication skills: the ability to use scientific language adequately to communicate the statistical methodologies employed and the results obtained. This skill will be stimulated by practical sessions and supplementary materials, including exercise sheets.
5) Learning skills: self-learning of new notions and more advanced statistical techniques, using additional materials and bibliography.

There are no specific requirements.
No preparatory courses are required.

1 Introduction to statistics 2 Statistical distributions 3 Graphical displays 4 Means 5 Variability 6 Shape 7 An overview of statistical summaries 8 Bivariate distributions: dependency 9 Bivariate distributions: regression 10 Bivariate distributions: correlation 11 Probability 12 Random variables 13 Some probability distributions 14 Law of large numbers and central limit theorem 15 Population, sample, sampling distributions 16 Point estimation 17 Interval estimation.

Cicchitelli, G., D'Urso, P., Minozzo, M. - Statistica. Principi e metodi. Quarta edizione (2022), Pearson.

In-class sessions comprise didactic lectures, practical sessions, hands-on exercises, demonstrations, discussion.
Lectures will be aimed at stimulating both interaction with students and their problem solving skills. Therefore, each topic will be supplemented by examples and hands-on exercises in order to facilitate the understanding of statistical tools and their use in social issues.
The textbook comes with an online platform providing tutoring for the exercises and self-assessment tools. This will facilitate students in preparation for the exam.

Lecture attendance is not mandatory but highly recommended given the know-how-oriented course setting.

The evaluation is performed by a final written examination, carried out during the scheduled exam sessions (3 calls in June / July session, 1 call in the September session, 2 calls in January / February session).
The written exam consists of 21 exercises with both theoretical and practical questions. The test is intended to assess knowledge and understanding and the student's ability to apply knowledge and understanding.
The student must indicate the correct answer and return the calculations necessary to obtain the indicated result.
For completing the test, the students will have 75 minutes and can use a calculator and statistical tables.
In itinere evaluation will be performed. The course includes two partial exams. The first partial exam, covering univariate and bivariate descriptive statistics, consists of 14 questions including both theoretical and practical (exercises) items. The second partial exam, covering inferential statistics, consists of 7 questions including both theoretical and practical (exercises) items.
Each correctly, thoroughly, and comprehensively answered question will be assigned a score (1 or 2 points depending on the difficulty of the question). The grade for each partial exam will be the sum of the scores obtained for each question.
The rules for the two partial exams are as follows:
1. To pass the exam, it is necessary to achieve a passing grade in both partial exams.
2. Access to the second partial exam is permitted only if the first partial exam has been passed.
3. If the first partial exam is passed but the grade is rejected, the student must take the full exam in one of the official exam sessions.
4. If both partial exams are passed, the exam will be officially recorded with a grade equal to the sum of the grades from the two partial exams. If the grade is rejected, the student must take the full exam in one of the official exam sessions.
For the partial exams, students will have 45 minutes and may use a calculator and statistical tables.

In determining the final grade, the assessment takes into account the following elements:
1. the thought process followed by the student in solving the proposed questions;
2. the correctness of the procedure chosen by the student to get the solution;
3. the adequacy of each solution proposed by the student, considering both the type of question and his expected competences;
4. the use of a correct and proper language.

A grade of at least 18/30 is required to pass the exam. Students must demonstrate a) to have acquired a sufficient knowledge of the topics covered in the course and b) to be able to identify statistical techniques and tools - simple but adequate - for the solution of the proposed real problems.
The grade 30/30 cum laude is assigned to those students who demonstrate an excellent knowledge of all the topics covered during the course and strong critical thinking skills. Students must also demonstrate to be able to identify the most suitable statistical techniques and tools, both simple and complex, for solving real problems.

1) The arithmetic mean and the median of the distribution of a variable Z observed on N = 950 statistical units are μ = 12.3 and m = 13, respectively. Knowing that the relationship linking variable W to variable Z is as follows: W = 5 + 0.8Z, calculate the arithmetic mean of variable W.
2) The arithmetic mean and the median of the distribution of a variable Z observed on N = 950 statistical units are μ = 12.3 and m = 13, respectively. Knowing that the relationship linking variable W to variable Z is as follows: W = 5 + 0.8Z, calculate the median of variable W.
3) It is known that the total sum of the science test grades in class 4B is 243 and deviance is 95.3. In class 4C of the same high school (27 students), the deviance is 115.4, with a total sum of grades equal to 226.8. Indicate in which of the two classes there is greater variability in the grades.
4) A sample of 35 mother-daughter pairs was asked at what age they started wearing makeup. The data obtained are as follows: Mean age of the mothers = 15.2 years; Mean age of the daughters = 13.8 years; Variance of the mothers' age = 2.25 years²; Variance of the daughters' age = 1.96 years²; Covariance between the age of the mother and that of the daughter = 0.84. Estimate the regression line for the age of the mother (X) and that of the daughter (Y).
5) Two balls are extracted with replacement from an urn containing 10 green balls, 18 blue balls, and 22 yellow balls. Calculate the probability of extracting a blue ball on the first draw and a yellow ball on the second draw.
6) The weight of water bottles follows a normal distribution, with a mean weight of 1.2 kg and a variance of 0.25 kg². If a bottle is chosen at random, what is the probability that its weight is less than 1.1 kg?
7) The time taken by students at a school to complete a reading comprehension test (in minutes) follows a normal distribution. In a sample of 100 students, the mean time recorded is 46 minutes, with a sample variance of 36. Determine the 95% confidence interval for the mean time taken.

• Topic 1 (10 hours). Describing univariate data: 1) Introduction to statistics; 2) Statistical distributions; 3) Graphical displays
  • Books: Statistica: principi e metodi, Chapters 1, 2 and 3


• Topic 2 (10 hours). Describing univariate data: 4) Means
  • Books: Statistica: principi e metodi, Chapter 4


• Topic 1 (10 hours). Describing univariate data: 5) Variability; 6) Shape; 7) An overview of statistical summaries
  • Books: Statistica: principi e metodi, Chapters 5, 6 and 7


• Topic 4 (8 hours). Describing the relation between two variables: 8) Bivariate distributions: dependency
  • Books: Statistica: principi e metodi, Chapter 9


• Topic 5 (8 hours). Describing the relation between two variables: 9) Bivariate distributions: regression; 10) Bivariate distributions: correlation
  • Books: Statistica: principi e metodi, Chapters 10 and 11


• Topic 6 (6 hours). Probability
  • Books: Statistica: principi e metodi, Chapter 12


• Topic 7 (10 hours). Inferential statistics: Random variables; Some probability distributions
  • Books: Statistica: principi e metodi, Chapter  13, 14 and 16


• Topic 8 (6 hours). Inferential statistics: Population, sample, sampling distributions; Point estimation
  • Books: Statistica: principi e metodi, Chapters 17 and 18


• Topic 9 (4 hours). Inferential statistics: Interval estimation
  • Books: Statistica: principi e metodi, Chapter 19